Question

Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then :

• A. g'=3g
• B. g'=\(\frac{g}{9}\)
• C. g'=9g
• D. g'=\(\frac{g}{3}\)

Answer 1

The Correct Option is A

Let the mass and radius of the new planet be M′ and R′, then for same density as earth,
R′=3R
M′=27M
we know M\(\propto\)V, where V\(\propto\)R³
For Earth 

g=\(\frac{GM}{R^2}\)  (1)

and for new planet

g'=\(\frac{GM'}{R^2}\)

=\(\frac{G(27M)}{(3R)^2}\)

=\(3\bigg(\frac{GM}{R^2}\bigg)\)=3g

\(\Rightarrow\) g'=3g

Therefore, the correct option is (A): g'=3g